Answer
$x\sqrt{2} + \sqrt{14}$
Work Step by Step
RECALL:
(1) Distributive Property:
For any real numbers a, b, and c,
$a(b+c) = ab+ ac$
(2) For any real numbers real numbers a and b within the domain,
$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$
Use rule (1) above to obtain:
$=\sqrt{2} \cdot x + \sqrt{2} \cdot \sqrt{7}
\\=x\sqrt{2} + \sqrt{2} \cdot \sqrt{7}$
Use rule (2) above to obtain:
$=x\sqrt{2} + \sqrt{2 \cdot 7}
\\=x\sqrt{2} + \sqrt{14}$
